Integrated services over a shared satellite channel need a MAC protocol that is able to deal with real-time tra$c without substantially a!ecting the e$ciency of the shared medium. Due to its bursty nature, MPEG coded VBR video transmission is one of the most challenging real-time applications. In this paper, we analyse the statistical performance of a simple allocation method for VBR traffic by using an accurate statistical model of an MPEG-2 VBR coded movie, whose tra$c exhibits a peak to mean ratio of about 4. The results were obtained both analytically and by simulation, and show that our method is suitable for transmitting non-interactive video and best-e!ort traffic on the same satellite link. The efficiency of the proposed method shows no dependency on the statistical properties of the input traffic.